10=7x+3x^2

Solution for 10=7x+3x^2 equation:

10=7x+3x^2

We move all terms to the left:

10-(7x+3x^2)=0

We get rid of parentheses

-3x^2-7x+10=0

a = -3; b = -7; c = +10;
Δ = b2-4ac
Δ = -72-4·(-3)·10
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*-3}=\frac{-6}{-6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*-3}=\frac{20}{-6}
=-3+1/3
$